Phase transitions in a MgB<Subscript>2</Subscript> granular BCS superconductor in weak magnetic fields

The character of temperature dependences of the electric conductivity of MgB₂ granular BCS superconductors at temperatures of ~35–45 K in external magnetic fields H _ext of up to ~2 kOe is studied. An increase in the superconducting transition width ΔT _c with an increase in Hext is found. The presence of a system of weak links in MgB₂-based granular superconductors is established. On the basis of experimental data, MgB₂ granular superconductor is assigned to two-level superconducting systems and the H–T phase diagram is constructed.     

Enhancement of pseudogap anomalies induced by nanoscale structural inhomogeneity in YBa<Subscript>2</Subscript>Cu<Subscript>3</Subscript>O<Subscript>6.93</Subscript> high-<Emphasis Type="Italic">T</Emphasis><Subscript>c</Subscript> superconductor

The magnetization M(H) in the superconducting state, dc magnetic susceptibility χ(T) in the normal state, and specific heat C(T) near the superconducting transition temperature T _c have been measured for a series of fine-crystalline YBa₂Cu₃O _y samples having nearly optimum values of y = 6.93 ± 0.3 and T _c = (91.5 ± 0.5) K. The samples differ only in the degree of nanoscale structural inhomogeneity. The characteristic parameters of superconductors (the London penetration depth and the Ginzburg–Landau parameter) and the thermodynamic critical field H _c are determined by the analysis of the magnetization curves M(H). It is found that the increase in the degree of nanoscale structural inhomogeneity leads to an increase in the characteristic parameters of superconductors and a decrease in H _c(T) and the jump of the specific heat ΔC/T _c. It is shown that the changes in the physical characteristics are caused by the suppression of the density of states near the Fermi level. The pseudogap is estimated by analyzing χ(T). It is found that the nanoscale structural inhomogeneity significantly enhances and probably even creates the pseudogap regime in the optimally doped high-T _c superconductors.     

Anomalous low-temperature behavior of the thermal characteristics of MgB<Subscript>2</Subscript>

We have studied the behavior of the thermal expansion coefficient α(T) (in a zero magnetic field and at H≈4 T), the heat capacity C(T), and the thermal conductivity κ(T) of magnesium boride (MgB₂) in the vicinity of T_c and at lower temperatures. It was established that MgB₂, like oxide-based high-temperature superconductors, exhibits a negative thermal expansion coefficient at low temperatures. The anomaly of α(T) in MgB₂ is significantly affected by the magnetic field. It was established that, in addition to the well-known superconducting transition at T_c≈40 K, MgB₂ exhibits an anomalous behavior of both heat capacity and thermal conductivity in the region of T≈10–12 K. The anomalies of C(T) and κ(T) take place in the same temperature interval where the thermal expansion coefficient of MgB₂ becomes negative. The low-temperature anomalies are related to the presence of a second group of charge carriers in MgB₂ and to an increase in the density of the Bose condensate corresponding to these carriers at T_c2≈10–12 K.     

Pseudogap and its temperature dependence in YBCO from the data of resistance measurements

The temperature dependence of the excess conductivity Δσ for Δσ = A(1 ? T/T^*)exp(Δ^*/T) (YBCO) epitaxial films is analyzed. The excess conductivity is determined from the difference between the normal resistance extrapolated to the low-temperature range and the measured resistance. It is demonstrated that the temperature dependence of the excess conductivity is adequately described by the relationship Δσ = A(1 ? T/T^*)exp(Δ^*/T). The pseudogap width and its temperature dependence are calculated under the assumption that the temperature behavior of the excess conductivity is associated with the formation of the pseudogap at temperatures well above the critical temperature T _c of superconductivity. The results obtained are compared with the available experimental and theoretical data. The crossover to fluctuation conductivity near the critical temperature T _c is discussed.     

The structure of a vortex line and the lower critical field in superconducting alloys

The structure of an isolated vortex line, and the lower critical fieldH _c 1, is calculated by means of the generalized Ginzburg-Landau (GL) theory for arbitrary values of the GL-parameterk(≧1/√2) and the mean free pathl at temperaturesT in the vicinity ofT _c . The free energy functional including the corrections of order [1?(T/T _c )] to the GL-functional is derived exactly. The corresponding Euler-Lagrange equations determining the zero-order (GL) contributions and the corrections of order [1?(T/T _c )] to the order parameter,f(r), and the superfluid velocity,v(r), have been solved numerically. The shapes of the first-order corrections off(r), v(r), and the magnetic field,h(r) are found to depend markedly, for a given value ofκ, on a second parameter,α=0.882(ξ ₀ /l) (whereξ ₀ is theBCS-coherence-distance). The deviations from the GL-solutions become largest forh(r) at parameter valuesk≈ 1 andα ≈ 0(the deviation ofh(0) is about 6% atT=0.9T _c forκ=1 andα=0). The ratioH _c1/H _c (where the thermodynamic criticalH _c has the BCS-temperature-dependence) is found to increase slightly in the “clean” limit (α=0), and to decrease slightly in the “dirty” limit (α=∞) asT decreases (the variation ofH _c 1/H _c is always less than 3% for arbitrary values ofκ andα asT decreases fromT _c to 0.9T _c ).     

The anisotropic conductivity of two-dimensional electrons on a half-filled high Landau evel

We study the conductivity of two-dimensional interacting electrons on the half-filled Nth Landau level with N?1 in the presence of quenched disorder. The existence of the unidirectional charge-density wave state at temperature T<T _c , where T _c is the transition temperature, leads to the anisotropic conductivity tensor. We find that the leading anisotropic corrections are proportional to (T _c ?T)/T _c just below the transition, in accordance with the experimental findings. Above T _c , the correlations corresponding to the unidirectional charge-density wave state below T _c result in corrections to the conductivity proportional to \(\sqrt {{{T_c } \mathord{\left/ {\vphantom {{T_c } {T - T_c }}} \right. \kern-\nulldelimiterspace} {T - T_c }}} \).     

Holographic Superconductor of Regular Phantom Black Hole

Holographic superconductors containing a non-minimal derivative coupling for the scalar field in a regular phantom plane symmetric black hole have been considered. We show that the parameter of the regular black hole b as well as the non-minimal derivative coupling parameter η affect the formation of the condensate as well as the conductivity in the superconductor. Moreover, b has a critical value in which the critical temperature T_c increases without a bound.     

Mössbauer study of the magnetocaloric compound AlFe<Subscript>2</Subscript><Emphasis Type="Bold">B</Emphasis><Subscript>2</Subscript>

Mössbauer spectroscopy in the ferromagnetic AlFe₂ B ₂ reveals T_c=299 K and shows good agreement with magnetic measurements. The crystals are plate-shaped. The flakes are found from X-ray diffraction to be in the crystallographic ac-plane in the orthorhombic system. The axes of the principle electric field gradient tensor are, by symmetry, colinear with the crystal a-, b- and c-axes. By using information about the quadrupole splitting and line asymmetry in the paramagnetic regime together with the quadrupole shift of the resonance lines in the ferromagnetic regime the magnetic hyperfine field direction is found to be in the ab-plane having an angle =40^° to the b-axis.     

Critical magnetic field of the vortex-free state in NbC thin films and prospects for its observation in MgB<Subscript>2</Subscript>

The critical magnetic fields H _c‖ and H _c2 are measured for thin films of the isotropic superconductor NbC. It is revealed that the critical fields exhibit strong anisotropy due to the vortex-free state of the film in a magnetic field aligned parallel to its surface. The H _c‖/H _c2 ratio at 2 K exceeds 6 and increases with increasing temperature. The dependence H _c‖(T) agrees quantitatively with the concepts of microscopic theory on the vortex-free state of a thin film of a clean superconductor in the temperature range below T _c . As the electron mean free path decreases under irradiation of the film with a low dose of He⁺ ions, the critical field H _c‖ remains unchanged near T _c but increases significantly at lower temperatures. The well-known theoretical models are used to estimate the electronic parameters and thicknesses of MgB₂ films for which the specific features associated with the vortex-free state of the two-gap superconductor can manifest themselves in the temperature dependence of the critical magnetic field H _c‖(T).     

On the Hall effect in a two-dimensional doped antiferromagnet

The conductivity and the Hall coefficient of a doped 2D antiferromagnet in the normal state are considered using the Kondo lattice model in the multimoment approximation. The anomalous temperature dependence of the kinetic coefficients is explained by the strong anisotropic charge-carrier scattering from the spin subsystem and found to be in qualitative agreement with the experimental data for the normal state of high-T _c superconductors.     

Variable-range cotunneling and conductivity of a granular metal

The Efros-Shklovskii (E-S) law for the conductivity of granular metals is interpreted as a result of a variable-range cotunneling process. The cotunneling between distant resonant grains is predominantly elastic at low T ≤ T _c , while it is inelastic (i.e., accompanied by creation of electron-hole pairs on a string of intermediate non-resonant grains) at T ≥ T _c . The corresponding E-S temperature T _ES , in the latter case, is slightly (logarithmically) T dependent. The magnetoresistance in the two cases is different: it may be relatively strong and negative at T?T _c , while, at T > T _c , it is suppressed due to inelastic processes, which destroy the interference.     

Robustness of <Emphasis Type="Italic">s</Emphasis>-wave pairing symmetry in iron-based superconductors and its implications for fundamentals of magnetically driven high-temperature superconductivity

Based on the assumption that the superconducting state belongs to a single irreducible representation of lattice symmetry, we propose that the pairing symmetry in all measured iron-based superconductors is generally consistent with the A _1g s-wave. Robust s-wave pairing throughout the different families of iron-based superconductors at different doping regions signals two fundamental principles behind high-T _c superconducting mechanisms: (i) the correspondence principle: the short-range magnetic-exchange interactions and the Fermi surfaces act collaboratively to achieve high-T _c superconductivity and determine pairing symmetries; (ii) the magnetic-selection pairing rule: superconductivity is only induced by the magnetic-exchange couplings from the super-exchange mechanism through cation-anion-cation chemical bonding. These principles explain why unconventional high-T _c superconductivity appears to be such a rare but robust phenomena, with its strict requirements regarding the electronic environment. The results will help us to identify new electronic structures that can support high-T _c superconductivity.     

Low-temperature anomalies in the specific heat and thermal conductivity of MgB<Subscript>2</Subscript>

The temperature dependences of the specific heat C(T) and thermal conductivity K(T) of MgB₂ were measured at low temperatures and in the neighborhood of T _c . In addition to the well-known superconducting transition at T _c ≈40 K, this compound was found to exhibit anomalous behavior of both the specific heat and thermal conductivity at lower temperatures, T≈10–12 K. Note that the anomalous behavior of C(T) and K(T) is observed in the same temperature region where MgB₂ was found to undergo negative thermal expansion. All the observed low-temperature anomalies are assigned to the existence in MgB₂ of a second group of carriers and its transition to the superconducting state at T_c2≈10?12 K.     

Polarization effects induced by a magnetic field in intrinsically granular superconductors

Based on the previously suggested model of nanoscale dislocation-induced Josephson junctions and their arrays, we study the magnetic-field-induced electric polarization effects in intrinsically granular superconductors. In addition to the new phenomenon of chemomagnetoelectricity, the model also predicts a few other interesting effects, including charge analogs of Meissner paramagnetism (at low fields) and a “fishtail” anomaly (at high fields). The conditions under which these effects can be experimentally measured in nonstoichiometric high-T_c superconductors are discussed.     

Temperature dependence of the upper critical field of superconducting alloys

The upper critical field,H _c2, is calculated in the temperature range close toT _c for arbitrary values of the mean free path 1. The method is to treat the fourth-order term in the linearized differential equation for the gap parameter as a perturbation to the harmonic oscillator equation. The Nambu-Tuan term, which determines the structure of the “clean-limit” and “dirty-limit” parts of the fourth-order term, is calculated by means of the ladder diagram technique for impurity interaction lines. The result is that the magnitude of the slope of the curveH _c2/√2H _c κ versust=T/T _c att=1 decreases monotonically from the value 0.41 to 0.12 as the ratio of the BCS coherence lengthξ ₀ to the mean free path 1 increases from 0 to ∞. For 1?ξ ₀ this slope is about 0.26.     

Temperature dependence of the surface upper critical field of superconducting alloys

The temperature dependence of the surface upper critical field,H _c3, nearT _c is calculated for arbitrary values of the mean free pathl by taking into account the fourthorder term of the generalized Ginzburg-Landau theory. For finitel the boundary condition is modified such that the normal derivative of the energy gap at the surface becomes positive. The slope of the curveH _c3/H _c2 versust=T/T _c att=1 is found to decrease monotoneously from zero to ?1.040 as one goes from the “dirty” to the “clean” limit.     

Field Confinement Energy at a Nonlinear Interface between Nonlinear Defocusing Media

The dependences of the resistance of the layered quasi-one-dimensional semiconductor TiS₃ on the direction and magnitude of the magnetic field B have been measured. The anisotropy and angular dependences of the magnetoresistance indicate the two-dimensional character of the conductivity at T < 100 K. Below T₀ ≈ 50 K, the magnetoresistance for the directions of the field in the plane of the layers (ab plane) increases sharply, whereas the transverse magnetoresistance (B ∥ c) becomes negative. The results confirm the possibility of an electron phase transition to a collective state at T₀. The negative magnetoresistance (at B ∥ c) below T₀ is explained by the magnetic-field-induced suppression of two-dimensional weak localization. The positive magnetoresistance (at B ∥ ab) is explained by the effect of the magnetic field on the spectrum of electronic states.     

Anion height dependence of <Emphasis Type="Italic">T</Emphasis><Subscript><Emphasis Type="Italic">c</Emphasis></Subscript> and the density of states in iron-based superconductors

Systematic ab initio LDA calculations were performed for all the typical representatives of recently discovered class of iron-based high-temperature superconductors: REOFe(As,P) (RE = La, Ce, Nd, Sm, Tb), Ba₂Fe₂As, (Sr,Ca)FFeAs, Sr₄Sc₂O₆Fe₂P₂, LiFeAs and Fe(Se,Te). Non-monotonic behavior of total density of states at the Fermi level is observed as a function of anion height relative to Fe layer with maximum at about Δz _a ～ 1.37 Å, attributed to changing Fe-As (P, Se, Te) hybridization. This leads to a similar dependence of superconducting transition temperature T _c as observed in the experiments. The fit of this dependence to elementary BCS theory produces semiquantitative agreement with experimental data for T _c for the whole class of iron-based superconductors. The similar fit to Allen-Dynes formula underestimates T _c in the vicinity of the maximum, signifying the possible importance of non-phonon pairing in this region. These results unambiguously demonstrate that the main effect of T _c variation between different types of iron-based superconductors is due to the corresponding variation of the density of states at the Fermi level.     

Upper critical field of cellular magnesium diboride

A cellular superconducting material consisting of thin (1–20 μm) MgB_2?x layers and magnesium granules of about 100 μm has been produced. The critical temperature T _c of this superconductor decreases with the thickness of the MgB_2?x layers. In unalloyed magnesium diboride, the curvature of the temperature dependence of the upper critical field H _c2(T) changes gradually from downward to pronounced upward as the temperature T _c decreases from 38 to 36 K.     

Enhancement of superconductivity in disordered films by parallel magnetic field

We show that the superconducting transition temperature T _c (H) of a very thin highly disordered film with strong spin-orbital scattering can be increased by a parallel magnetic field H. This effect is due to the polarization of magnetic impurity spins, which reduces the full exchange scattering rate of electrons; the largest effect is predicted for spin-1/2 impurities. Moreover, for some range of magnetic impurity concentrations, the phenomenon of superconductivity induced by magnetic field is predicted: the superconducting transition temperature T _c (H) is found to be nonzero in the range of magnetic fields 0 < H* ≤ H ≤ H _c .